The government has imposed a fine on the Corner Tavern.The fine calls for annual payments of $125,000,$100,000,$75,000,and $50,000,respectively,over the next four years.The first payment is due one year from today.The government plans to invest the funds until the final payment is collected and then donate the entire amount,including the investment earnings,to help the local community shelter.The government will earn 5.5 percent on the funds held.How much will the community shelter receive four years from today?

Question

Quizplus · Accepted Answer

First, we need to calculate the future value of the payments and the interest earned on them. Using the formula:

FV = Payment * [(1 + r)^n - 1] / r

where r is the annual interest rate and n is the number of periods (in this case, 4), we get:

FV(125,000) = 530,266.08 
FV(100,000) = 424,212.86 
FV(75,000) = 318,159.63 
FV(50,000) = 212,106.41

Next, we add up these amounts to get the total future value:

Total FV = 1,484,745.98

Finally, we need to calculate the interest earned on this amount over four years at 5.5 percent:

Interest = Total FV * (1 + r)^n - Total FV 
= 164,764.01

The total amount the community shelter will receive in four years is:

Total = Total FV + Interest 
= 1,649,510.99

Therefore, the best choice is C ($392,510.99).

The Government Has Imposed a Fine on the Corner Tavern